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          LRU缓存算法
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        <h3 id="一、LRU简介"><a href="#一、LRU简介" class="headerlink" title="一、LRU简介"></a>一、LRU简介</h3><p>&ensp;&ensp;&ensp;&ensp;LRU算法全称是最近最少使用算法（Least Recently Use），广泛的应用于缓存机制中。当缓存使用的空间达到上限后，就需要从已有的数据中淘汰一部分以维持缓存的可用性，而淘汰数据的选择就是通过LRU算法完成的。</p>
<span id="more"></span>

<p>&ensp;&ensp;&ensp;&ensp;LRU算法的基本思想是基于局部性原理的时间局部性：</p>
<blockquote>
<p>  如果一个信息项正在被访问，那么在近期它很可能还会被再次访问。</p>
</blockquote>
<p>&ensp;&ensp;&ensp;&ensp;所以顾名思义，LRU算法会选出最近最少使用的数据进行淘汰。</p>
<p><strong>原理：</strong></p>
<p>&ensp;&ensp;&ensp;&ensp;一般来讲，LRU将访问数据的顺序或时间和数据本身维护在一个容器当中。当访问一个数据时：</p>
<ol>
<li> 该数据不在容器当中，则设置该数据的优先级为最高并放入容器中。</li>
<li> 该数据在容器当中，则更新该数据的优先级至最高。</li>
</ol>
<p>&ensp;&ensp;&ensp;&ensp;当数据的总量达到上限后，则移除容器中优先级最低的数据。下图是一个简单的LRU原理示意图：</p>
<p><img src="/myblog/2021/06/06/%E6%95%B0%E6%8D%AE%E7%BB%93%E6%9E%84%EF%BC%9ALRU%E7%BC%93%E5%AD%98/1.png" alt="LRU原理示意图.jpg"></p>
<p>&ensp;&ensp;&ensp;&ensp;如果我们按照<code>7 0 1 2 0 3 0 4</code>的顺序来访问数据，且数据的总量上限为3，则如上图所示，LRU算法会依次淘汰<code>7 1 2</code>这三个数据。</p>
<h3 id="二、设计LRU"><a href="#二、设计LRU" class="headerlink" title="二、设计LRU"></a>二、设计LRU</h3><p><strong>题目：</strong></p>
<blockquote>
<p>&ensp;&ensp;&ensp;&ensp;运用你所掌握的数据结构，设计和实现一个 <a target="_blank" rel="noopener" href="https://baike.baidu.com/item/LRU">LRU (最近最少使用) 缓存机制</a> 。</p>
<p>实现 <code>LRUCache</code> 类：</p>
<ul>
<li>  <code>LRUCache(int capacity)</code> 以正整数作为容量 <code>capacity</code> 初始化 LRU 缓存</li>
<li>  <code>int get(int key)</code> 如果关键字 <code>key</code> 存在于缓存中，则返回关键字的值，否则返回 <code>-1</code> 。</li>
<li>  <code>void put(int key, int value)</code> 如果关键字已经存在，则变更其数据值；如果关键字不存在，则插入该组「关键字-值」。当缓存容量达到上限时，它应该在写入新数据之前删除最久未使用的数据值，从而为新的数据值留出空间。</li>
</ul>
<p><strong>进阶</strong>：你是否可以在 <code>O(1)</code> 时间复杂度内完成这两种操作？</p>
<p><strong>提示：</strong></p>
<ul>
<li>  <code>1 &lt;= capacity &lt;= 3000</code></li>
<li>  <code>0 &lt;= key &lt;= 3000</code></li>
<li>  <code>0 &lt;= value &lt;= 104</code></li>
<li>  最多调用 <code>3 * 104</code> 次 <code>get</code> 和 <code>put</code></li>
</ul>
</blockquote>
<p><strong>设计思路：</strong></p>
<p>&ensp;&ensp;&ensp;&ensp;1、显然 <code>cache</code> 中的元素必须有时序，以区分最近使用的和久未使用的数据，当容量满了之后要删除最久未使用的那个元素腾位置。</p>
<p>&ensp;&ensp;&ensp;&ensp;2、我们要在 <code>cache</code> 中快速找某个 <code>key</code> 是否已存在并得到对应的 <code>val</code>；</p>
<p>&ensp;&ensp;&ensp;&ensp;3、每次访问 <code>cache</code> 中的某个 <code>key</code>，需要将这个元素变为最近使用的，也就是说 <code>cache</code> 要支持在任意位置快速插入和删除元素。</p>
<p>&ensp;&ensp;&ensp;&ensp;LRU 缓存算法的核心数据结构就是哈希链表，双向链表和哈希表的结合体。这个数据结构长这样：</p>
<img src="/myblog/myblog/2021/06/06/%E6%95%B0%E6%8D%AE%E7%BB%93%E6%9E%84%EF%BC%9ALRU%E7%BC%93%E5%AD%98/2.png" alt="image-20210322145136153" style="zoom:50%;">

<p>&ensp;&ensp;&ensp;&ensp;1、如果我们每次默认从链表尾部添加元素，那么显然越靠尾部的元素就是最近使用的，越靠头部的元素就是最久未使用的。</p>
<p>&ensp;&ensp;&ensp;&ensp;2、对于某一个 <code>key</code>，我们可以通过哈希表快速定位到链表中的节点，从而取得对应 <code>val</code>。</p>
<p>&ensp;&ensp;&ensp;&ensp;3、链表显然是支持在任意位置快速插入和删除的，改改指针就行。只不过传统的链表无法按照索引快速访问某一个位置的元素，而这里借助哈希表，可以通过 <code>key</code> 快速映射到任意一个链表节点，然后进行插入和删除。</p>
<blockquote>
<p>对于 get 操作，首先判断 key 是否存在：</p>
<p>​    如果 key 不存在，则返回 -1−1；</p>
<p>​    如果 key 存在，则 key 对应的节点是最近被使用的节点。通过哈希表定位到该节点在双向链表中的位置，并将其移动到双向链表的头部，最后返回该节点的值。</p>
<p>对于 put 操作，首先判断 key 是否存在：</p>
<p>​    如果 key 不存在，使用 key 和 value 创建一个新的节点，在双向链表的头部添加该节点，并将 key 和该节点添加进哈希表中。然后判断双向链表的节点数是否超出容量，如果超出容量，则删除双向链表的尾部节点，并删除哈希表中对应的项；</p>
<p>​    如果 key 存在，则与 get 操作类似，先通过哈希表定位，再将对应的节点的值更新为 value，并将该节点移到双向链表的头部。</p>
</blockquote>
<p>代码：</p>
<figure class="highlight cpp"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br><span class="line">44</span><br><span class="line">45</span><br><span class="line">46</span><br><span class="line">47</span><br></pre></td><td class="code"><pre><span class="line"><span class="class"><span class="keyword">class</span> <span class="title">LRUCache</span> &#123;</span></span><br><span class="line"><span class="keyword">public</span>:</span><br><span class="line">    <span class="built_in">LRUCache</span>(<span class="keyword">int</span> capacity) : _capacity(capacity) &#123;&#125;</span><br><span class="line">    </span><br><span class="line">    <span class="function"><span class="keyword">int</span> <span class="title">get</span><span class="params">(<span class="keyword">int</span> key)</span> </span></span><br><span class="line"><span class="function">    </span>&#123;</span><br><span class="line">        <span class="keyword">auto</span> it = _hashTable.<span class="built_in">find</span>(key);</span><br><span class="line">        <span class="keyword">if</span>(it != _hashTable.<span class="built_in">end</span>())</span><br><span class="line">        &#123;</span><br><span class="line">            _list.<span class="built_in">splice</span>(_list.<span class="built_in">begin</span>(), _list, it-&gt;second);</span><br><span class="line">            <span class="keyword">return</span> it-&gt;second-&gt;second;</span><br><span class="line">        &#125;</span><br><span class="line">        <span class="keyword">return</span> <span class="number">-1</span>;</span><br><span class="line">    &#125;</span><br><span class="line">    </span><br><span class="line">    <span class="function"><span class="keyword">void</span> <span class="title">put</span><span class="params">(<span class="keyword">int</span> key, <span class="keyword">int</span> value)</span> </span></span><br><span class="line"><span class="function">    </span>&#123;</span><br><span class="line">        <span class="comment">// it 为 key 对应的迭代器（链表的），即 map 的 value</span></span><br><span class="line">        <span class="keyword">auto</span> it = _hashTable.<span class="built_in">find</span>(key);</span><br><span class="line">        <span class="keyword">if</span>(it != _hashTable.<span class="built_in">end</span>())</span><br><span class="line">        &#123;</span><br><span class="line">            _list.<span class="built_in">splice</span>(_list.<span class="built_in">begin</span>(), _list, it-&gt;second);</span><br><span class="line">            it-&gt;second-&gt;second = value;</span><br><span class="line">            <span class="keyword">return</span>;</span><br><span class="line">        &#125;</span><br><span class="line"></span><br><span class="line">        _list.<span class="built_in">emplace_front</span>(key,value);</span><br><span class="line">        _hashTable[key] = _list.<span class="built_in">begin</span>();</span><br><span class="line">        <span class="keyword">if</span>(_hashTable.<span class="built_in">size</span>() &gt; _capacity)</span><br><span class="line">        &#123;</span><br><span class="line">            _hashTable.<span class="built_in">erase</span>(_list.<span class="built_in">back</span>().first);</span><br><span class="line">            _list.<span class="built_in">pop_back</span>();</span><br><span class="line">        &#125;</span><br><span class="line">    &#125;</span><br><span class="line"></span><br><span class="line"><span class="keyword">private</span>:</span><br><span class="line">    unordered_map&lt;<span class="keyword">int</span>, list&lt;pair&lt;<span class="keyword">int</span>, <span class="keyword">int</span>&gt;&gt;::iterator&gt; _hashTable;</span><br><span class="line">    list&lt;pair&lt;<span class="keyword">int</span>, <span class="keyword">int</span>&gt;&gt; _list;</span><br><span class="line">    <span class="keyword">int</span> _capacity;</span><br><span class="line">&#125;;</span><br><span class="line"></span><br><span class="line"><span class="comment">/**</span></span><br><span class="line"><span class="comment"> * Your LRUCache object will be instantiated and called as such:</span></span><br><span class="line"><span class="comment"> * LRUCache* obj = new LRUCache(capacity);</span></span><br><span class="line"><span class="comment"> * int param_1 = obj-&gt;get(key);</span></span><br><span class="line"><span class="comment"> * obj-&gt;put(key,value);</span></span><br><span class="line"><span class="comment"> */</span></span><br></pre></td></tr></table></figure>

<p>&ensp;&ensp;&ensp;&ensp;这里主要需要好好理解list的splice这个方法</p>
<figure class="highlight plain"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><span class="line">void splice (iterator position, list&amp; x, iterator i);</span><br></pre></td></tr></table></figure>

<p>&ensp;&ensp;&ensp;&ensp;简单来说就是把 x 这个 list 的 i 处元素插入到 position 的位置。</p>
<p><a target="_blank" rel="noopener" href="https://mp.weixin.qq.com/s?__biz=MzAxODQxMDM0Mw==&mid=2247486428&idx=1&sn=3611a14535669ba3372c73e24121247c&chksm=9bd7f5d4aca07cc28c02c3411d0633fc12c94c2555c08cbfaa2ccd50cc2d25160fb23bccce7f&scene=21#wechat_redirect">手把手带你拆解 LRU 算法</a></p>
<p><a target="_blank" rel="noopener" href="https://juejin.cn/post/6844904049263771662">LRU算法及其优化策略——算法篇 (juejin.cn)</a></p>

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